My suspicion is that this "Brexit opportunities" job might be primarily a make-work thing cooked up as a way, without demoting him, of moving Reese-Mogg out of too much public attention in his House Leader role, where his prominence on TV is a bit much if Johnson is trying to redo his image, and look a bit more like a serious statesman. Some chance.
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Whether the numerous gatherings count as parties or not is totally irrelevant. The regulatiins never even used the word. Any kind of gathering - at times even more than two people - were forbidden, unless they were essential word meetings, with as few people involved as possible. Hell, you couldn't even sit down on a park bench at the height of it. Having anyone to visit in your personal flat was completely forbidden, for any reason..